How do you solve #(x + 7) ( 2x + 5) = - 7#?

2 Answers
Meave60
Jul 26, 2017

#x=-6,-7/2#

Explanation:

Solve:

#(x+7)(2x+5)=-7#

Expand the left side using the FOIL method.
http://www.mathcaptain.com/algebra/foil-method.html

#2x^2+19x+35=-7#

Add #7# to both sides.

#2x^2+19x+35+7=0#

Simplify.

#2x^2+19x+42=0#

Factor the left-hand side.

#(x+6)(2x+7)=0#

Set each binomial equal to zero and solve.

#(x+6)=0#

#x=-6#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#(2x+7)=0#

#2x=-7#

Divide both sides by #2#.

#x=-7/2#

Suren Abreu
Jul 26, 2017

#x=-7/2=-3 1/2# or #x=-6#

Explanation:

#(x+7)(2x+5)=-7#

Expand the brackets.

#x(2x+5)+7(2x+5)=-7#

#2x^2+5x+14x+35=-7#

#2x^2+19x+35=-7#

Add #7# to both sides.

#2x^2+19x+35+7=7-7#

#2x^2+19x+42=0#

Factorise.

#2x^2+12x+7x+42=0#

#2x(x+6)+7(x+6)=0#

#(2x+7)(x+6)=0#

#2x+7=0# and #x+6=0#

#x=-7/2# or #x=-6#

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